Since the output of an ADC is not a 12-bit bus but contained in two registers, you first need some mechanism to get that value into your component which is usually a job for DMA.

Several choices for squaring, easiest first:

The eoc-signal triggers your component (consisting of an interrupt and some software) to get that value and calculate the square. This will work only at lower sample-rates as some few kHz.

Here http://www.cypress.com/?app=forum&id=2492&rID=76712 you find some informations how to access a PSoC-internal component, a "multiply and accumulator" which could do the squaring within 18(!!!) clock cycles but is quite more complex to modify to your needs.

Last suggestion is to use VeriLog and program a datapath to do that job. This could do that task (shift and add) in 14 to 20 (guessed) clock cycles.

Get the examples, videos and appnotes for DMA

Get videos for component creation

When you decide to take "The Hard Way" using hardware (smile) look at "DataPath"

In the right-hand upper corner of this page is a keyword search which wil lead you to a bunch of documents and a large number of user-posts telling where you might run into troubles. (smile again)